A note on uniform observability

We prove that the classical inequality P/sub t//spl les//spl Oscr//sub t//sup -1/C/sub t/ relating the variance of the Kalman filter estimate, the observability matrix, and the controllability matrix is not true. This inequality is the cornerstone of the asymptotic stability theory of the Kalman filter for time-varying systems. We provide another inequality of the same type.